How is socialism represented in J. B. Priestley's play "An Inspector Calls" ?
Do you mean as an institution or as a philosophy? If you mean the latter, the inspector himself represents socialism (or rather its values) by knocking on the Birlings' door and asking for a personal reckoning of each person's dealings with the suicide victim in question (a poor, bewildered, and abandoned pregnant girl who kills herself by swallowing poison). The moral "in a nutshell" is that as members of society, we are all implicated and we are all responsible for the down-and-outers living on the fringe of our material world.
Socialism as an institution is not really represented since it is the capitalistic system that the author is criticizing.
Priestley's silver spoon preoccupation with the plight of the poor are reminiscent of Charles Dickens, Bernard Shaw and George Orwell (Eric Blair), all disgruntled with the inegality of wealth distribution and more particularly, with the flagrant disparity between word and deed of the social "do-gooders" of their times.
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